Modifiziertes Frisbee-ProblemQyQtSSV3aXRoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJLkxpbmVhckFsZ2VicmFHRiUhIiI=print(); # input placeholderDie Matrix der SpielsPkkiQUc2Ii1JJ01hdHJpeEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYlIiIkRis3JTclRisiIiIiIiE3JUYuIiIjRi43JUYvRjFGMQ==print(); # input placeholderDie ersten Potenzen dieser MatrixNistSSJeRyUqcHJvdGVjdGVkRzYkSSJBRzYiIiIiKiRGJyIiIyokRiciIiQqJEYnIiIlKiRGJyIiJiokRiciIicqJEYnIiIoKiRGJyIiKSokRiciIio=print(); # input placeholderJSFHCharakteristisches Polynom und 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print(); # input 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(); # input placeholderLUkmZXZhbGZHJSpwcm90ZWN0ZWRHNiNJIiVHNiI=print(); # input 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 ist dominierende Nullstelle!Vandermonde-Matrix der Nullstellen: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print(); # input placeholderMatrix der AnfangswertePkkiQkc2Ii1JJ01hdHJpeEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJDYjNyU3JSIiIiIiJCIjNTclIiIhRi0iIiY3JUYxRjFGLQ==print(); # input placeholderJSFHBestimmung der Koeffizienten f\303\274r die drei L\303\266sungenPkkiQ0c2Ii1JKlRyYW5zcG9zZUdGJDYjLUksTGluZWFyU29sdmVHRiQ2JC1GJjYjSSJWR0YkLUYmNiNJIkJHRiQ=print(); # input placeholderJSFHVektor der n-ten Potenzen der NullstellenPkkiUkc2ImYqNiNJIm5HRiRGJDYkSSlvcGVyYXRvckdGJEkmYXJyb3dHRiRGJC1JJDwsPkdJKF9zeXNsaWJHRiQ2JSkmSSdsYW1iZGFHRiQ2IyIiIjkkKSZGMTYjIiIjRjQpJkYxNiMiIiRGNEYkRiRGJA==print(); # input placeholderJSFHBerechnung der Anzahlen der Frisbee-Pfade der L\303\244nge n von 1 \342\207\235 i (i=1,2,3)
LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYvLUkjbWlHRiQ2JVEiRkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIn5GJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTC1GNjYtUSomY29sb25lcTtGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjc3Nzc3OGVtRicvRk5GU0Y1LUYsNiVRJ01hdHJpeEYnRi9GMi1JKG1mZW5jZWRHRiQ2JC1GIzYnLUkjbW5HRiQ2JFEiM0YnRjktRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSEZKL0ZOUSwwLjMzMzMzMzNlbUYnLUZobjYkUSMxMEYnRjkvJStleGVjdXRhYmxlR0Y9RjlGOS1GNjYtUSI6RidGOUY7Rj5GQEZCRkRGRkZIRlJGVEY1LUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHUSYwLjBlbUYnLyUmZGVwdGhHRl5wLyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUZqbzYmRlxwRl9wRmJwL0ZlcFElYXV0b0YnLUYsNiNRIUYnRmRvRjk=print(); # input 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(); # input placeholderLUkpc2ltcGxpZnlHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2JEkiRkdGJ0kpc3ltYm9saWNHRic=print(); # input placeholderJSFHJSFHAndere BetrachtungsweiseJSFHBetrachte statt A die MatrixPkkjQXNHNiIsJEkiQUdGJCMiIiIiIiU=print(); # input placeholderJSFHDie Matrix As ist ein stochastische Matrix ! Nichtnegative Koeffizienten und Zeilensummen = 1.NiUqJEkjQXNHNiIiIiMqJEYkIiIkKiRGJCIiJQ==print(); # input placeholderLUkmZXZhbGZHJSpwcm90ZWN0ZWRHNiMqJEkjQXNHNiIiIiY=print(); # input placeholderLUkmZXZhbGZHJSpwcm90ZWN0ZWRHNiMqJEkjQXNHNiIiIzU=print(); # input placeholderLUkmZXZhbGZHJSpwcm90ZWN0ZWRHNiMqJEkjQXNHNiIiIz8=print(); # input placeholderLUkmZXZhbGZHJSpwcm90ZWN0ZWRHNiMqJEkjQXNHNiIiI10=print(); # input placeholderLUkmZXZhbGZHJSpwcm90ZWN0ZWRHNiMqJEkjQXNHNiIiJCsiprint(); # input placeholderJSFHDie Matrizen LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1JJW1zdXBHRiQ2JS1GLDYlUSNBc0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GLDYlUSJuRidGN0Y6LyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0Y7USdub3JtYWxGJ0YrRkNGRg== konvergieren f\303\274r n \342\206\222 \342\210\236! Und zwar konvergieren alle drei Zeilen gegen denselben Vektor!
"stochastische Matrix" bedeutet (u.a.):
Der 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 ist Rechts-Eigenvektor zum Eigenwert \316\273=1.
As muss auch einen Links-Eigenvektor zum Eigenwert \316\273=1 haben.
Das ist der Vektor 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).LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2I1EhRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuMGVtRicvJSZkZXB0aEdGNC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GMDYmRjJGNUY4L0Y7USVhdXRvRictRiw2JVEtRWlnZW52ZWN0b3JzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiUtRiw2JVEjQXNGJ0ZERkcvJStleGVjdXRhYmxlR1EmZmFsc2VGJy9GSFEnbm9ybWFsRidGVUZSRlU=print(); # input placeholderLUktRWlnZW52ZWN0b3JzRzYiNiMtSSpUcmFuc3Bvc2VHRiQ2I0kjQXNHRiQ=print(); # input placeholderJSFHTTdSMApJNVJUQUJMRV9TQVZFLzQ5MDUzMjAwWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQiIiQiIiIiIiFGKCIiI0YqRilGKEYqRiY=TTdSMApJNVJUQUJMRV9TQVZFLzQ5MDUzMjAwWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQiIiQiIiIiIiFGKCIiI0YqRilGKEYqRiY=TTdSMApJNVJUQUJMRV9TQVZFLzExOTM1NzIwWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQiIzUiIiYiIiNGKCIiKCIiKSIiIiIiJSIiJ0YmTTdSMApJNVJUQUJMRV9TQVZFLzEyNzgzMDY0WCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQiI04iI0EiIzlGKCIjRiIjSSIiKCIjOiIjP0YmTTdSMApJNVJUQUJMRV9TQVZFLzQ4MjIxMDAwWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQiJEYiIiMkKiIjc0YoIiQxIiIkOSIiI08iI2QiI3FGJg==TTdSMApJNVJUQUJMRV9TQVZFLzQ2MjI5OTc2WCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQiJHUlIiQmUSIkSSRGKCIkPiUiJFMlIiRsIiIkPyMiJGEjRiY=TTdSMApJNFJUQUJMRV9TQVZFLzQwMDU4MDhYLCUpYW55dGhpbmdHNiI2IltnbCEiJSEhISMqIiQiJCIlMj0iJXU6IiVJOUYoIiVqOyIlPTwiJDooIiRmKSIkWypGJg==TTdSMApJNVJUQUJMRV9TQVZFLzEyNjIxNjMyWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQiJSYqcCIlJlEnIiUzZ0YoIiU9bSIlaW4iJS9JIiUiUSQiJTlPRiY=TTdSMApJNFJUQUJMRV9TQVZFLzMzOTE3MjBYLCUpYW55dGhpbmdHNiI2IltnbCEiJSEhISMqIiQiJCImcXQjIiZ0ZCMiJid5Q0YoIiYkUUUiJmduIyImJFI3IiYhUTgiJiEqUiJGJg==TTdSMApJNVJUQUJMRV9TQVZFLzQ5MDgzNDE2WCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQiJyQpeTUiJy1QNSInPTY1RigiJypIMCIiJydHMSIiJmYwJiImVkomIiZTWiZGJg==TTdSMApJNVJUQUJMRV9TQVZFLzQ3MDM0MTkyWCwlKWFueXRoaW5nRzYjJiUsVmFuZGVybW9uZGVHNiM3JSIiJSwmIyIiJCIiIyIiIiokIiImI0YvRi5GMiwmRixGL0YwIyEiIkYuNiJbZ2whIiUhISEjKiIkIiRGL0YvRi9GKkYrRjMiIzsqJEYrRi4qJEYzRi5GNg==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TTdSMApJNVJUQUJMRV9TQVZFLzEwODA5NDMyWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQjIiIkIiIlIyIiIkYpIiIhRiojRisiIiNGLUYsRipGLUYmTTdSMApJNVJUQUJMRV9TQVZFLzE0MzQyNDU2WCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQjIiImIiIpI0YoIiM7IyIiIkYpRiojIiIoRisjRi0iIiMjRi1GKyNGLSIiJSMiIiRGKUYmTTdSMApJNVJUQUJMRV9TQVZFLzQ2OTcwMTY4WCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQjIiNOIiNrIyIjNiIjSyMiIihGLEYqIyIjRkYpIyIjOkYsI0YuRikjRjJGKSMiIiYiIztGJg==TTdSMApJNVJUQUJMRV9TQVZFLzE2NTUyNzY4WCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQjIiRGIiIkYyMjIiMkKkYpIyIiKiIjS0YqIyIjYCIkRyIjIiNkRjEjRi0iI2sjRjNGKSMiI05GMUYmTTdSMApJNVJUQUJMRV9TQVZFLzEzNTQwOTIwWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQkIitdaSEqR1khIzUkIitEY3dmUEYpJCIrXWlsQUtGKUYqJCIrdm96IjQlRikkIisrXShvSCVGKSQiK0QiRzhoIkYpJCIrK3ZWW0BGKSQiK10oby9bI0YpRiY=TTdSMApJNVJUQUJMRV9TQVZFLzQ2NDU2MTEyWCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQkIitHbmB2UyEjNSQiK1B2OXJSRikkIitxOWoxUkYpRiokIitnMS02U0YpJCIrME9tTlNGKSQiK05kSmA+RikkIistPSR5LCNGKSQiK0VccWQ/RilGJg==TTdSMApJNVJUQUJMRV9TQVZFLzE0MTM3MjI0WCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQkIis1KCozLFMhIzUkIitvUGUqKlJGKSQiK1dJbCkqUkYpRiokIisoKSplLCslRikkIisiXDkwKyVGKSQiK0FsSyoqPkYpJCIrWXNEKz9GKSQiK2xDJDMrI0YpRiY=TTdSMApJNVJUQUJMRV9TQVZFLzEzMzU0Mzg0WCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQkIisuKysrUyEjNSQiKyoqKioqKioqUkYpJCIrJyoqKioqKipSRilGKiQiKysrKytTRikkIistKysrU0YpJCIrKSoqKioqKio+RikkIissKysrP0YpJCIrLSsrKz9GKUYmTTdSMApJNVJUQUJMRV9TQVZFLzQ5MzYyMjU2WCwlKWFueXRoaW5nRzYiNiJbZ2whIiUhISEjKiIkIiQkIisrKysrUyEjNUYnRidGJ0YnRickIisrKysrP0YpRipGKkYmTTdSMApJNVJUQUJMRV9TQVZFLzE1MjM3MzEyWColKmFsZ2VicmFpY0c2IjYiW2dsISMlISEhIiQiJCIiIiwmIyIiJCIiKUYnKiQiIiYjRiciIiMjRidGKywmRilGJ0YsIyEiIkYrRiY=TTdSMApJNVJUQUJMRV9TQVZFLzE1MjM3MTEyWCwlKmFsZ2VicmFpY0c2IjYiW2dsISIlISEhIyoiJCIkIiIiRidGJywkKiYsJiNGJyIiI0YnKiQiIiZGK0YrISIiLCYjISIkRixGJ0YtRitGL0YrLCQqJEYqRi9GK0YnLCQqJiwmRitGJ0YtI0YvRixGLywmRjFGJ0YtRjhGL0YrLCQqJEY3Ri9GK0YnRiY=TTdSMApJNVJUQUJMRV9TQVZFLzE1NjI0MjQ4WColKmFsZ2VicmFpY0c2IjYiW2dsISMlISEhIiQiJCIiIiwmIyIiJCIiKUYnKiQiIiYjRiciIiMjRidGKywmRilGJ0YsIyEiIkYrRiY=TTdSMApJNVJUQUJMRV9TQVZFLzE1ODEzMzY4WCwlKmFsZ2VicmFpY0c2IjYiW2dsISIlISEhIyoiJCIkIiIjRiciIiIqJiwmI0YoRidGKCokIiImRitGKyEiIiwmIyEiJEYnRihGLEYrRi4qJEYqRi5GKComLCZGK0YoRiwjRi5GJ0YuLCZGMEYoRixGNUYuKiRGNEYuRihGJg==